NANO LETTERS
First-Principles Studies of the Dynamics of [2]Rotaxane Molecular Switches
2009 Vol. 9, No. 9 3225-3229
Kinyip Phoa,† J. B. Neaton,‡ and Vivek Subramanian*,† Department of Electrical Engineering and Computer Sciences, UniVersity of California, Berkeley, California, 94720, and Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California, 94720 Received May 9, 2009; Revised Manuscript Received August 12, 2009
ABSTRACT Realization of controlled binary switching in individual molecules is of fundamental importance for nanoscale electronics where the use of molecular components promises the flexibility of engineering performance through controlled organic synthesis. The active component of the [2]rotaxane molecule consists of a cyclobis-(paraquat-p-phenylene) ring-shaped structure [(CBPQT4+)(PF6-)4], proposed to switch between two stations, tetrathiafulvalene (TTF) and 1,5-dioxynapthalene (DNP), that lie along a common molecular backbone. However, there are still several open questions regarding their operation and performance, particularly in a device geometry. In this work, the switching speed of crossbar array devices based on [2]rotaxane arrays is studied with first principles density functional theory (DFT). The energetics of a likely configurational pathway for the CBPQT-ring shuttling along the molecular backbone between stations is computed and analyzed, as are ionization potentials and electrostatic screening properties. From these quantities, a new switching mechanism is identified. The applied bias at the cathode alters the energy landscape, making the OFF-state configuration energetically unfavorable relative to the ON-state without involving charging, as previously suggested.1 For a crossbar memory array of reasonable size, the calculations predict that the switching speed is dominated by the shuttling time of the CBPQT-ring, which is estimated to be a few microseconds. The applicability of this technology is discussed in light of this result.
In 2002, Heath and Stoddart reported the first molecular memory in a crossbar array structure.2 In this architecture, a [2]rotaxane monolayer was sandwiched between a titanium/ aluminum top electrode and an n-type silicon bottom electrode at each crossbar junction. Figure 1a shows the [2]rotaxane molecule, after ref 2, while Figure 1b depicts a cartoon of its low-conductance OFF-state, where the cyclobis(paraquat-p-phenylene) tetracation (CBPQT) ring is at the tetrathiafulvalene (TTF) station, and Figure 1c illustrates the proposed high-conductance ON-state with the CBPQT ring residing near the 1,5-dioxynaphthalene (DNP) station. It has been previously hypothesized that the CBPQT ring would traverse from TTF to DNP when a +2 V bias was applied on an n-type silicon bottom electrode, switching the molecule from OFF- to ON-state.2 Hysteresis curves and tens of cycles of repeated switching between these two states were measured.2 These experiments prompted several subsequent theoretical studies of conductance,3,4 packing density,5,6 ionization potentials (IP),1 and the density of states (DOS)1 for [2]rotaxane and its simpler constituent molecules. In part on the basis of these calculations, a mechanism for how this * To whom correspondence should be addressed. E-mail: viveks@eecs. berkeley.edu. † University of California. ‡ Lawrence Berkeley National Laboratory. 10.1021/nl901478a CCC: $40.75 Published on Web 08/25/2009
2009 American Chemical Society
molecule would switch between its two stable coconformations has also been proposed.1 However, one of the most important figures of merit, the switching speed, or the average rate that the CBPQT ring may alternate between ON and OFF states, has been discussed only recently.7 Here, using information from first principles calculations, an estimate of this time scale is provided as the sum of two contributions, the shuttling time of the CBPQT ring, tshuttle, and the RC time constant of the array, tRC. Estimating tshuttle requires an accurate picture of an energy landscape of the “shuttling” reaction, which is computed for different configurations of [2]rotaxane along a realistic reaction coordinate, as shown in Figure 2. To compare with a previously proposed switching mechanism,1 the IPs of the [2]rotaxane molecule are also computed, which critically affects the switching time but was not discussed in previous studies.7 The RC time constant tRC is estimated from resistance R of the electrodes, and the capacitance C of the crossbar junction, which can be evaluated from the computed dielectric properties of the molecule in its OFFand ON-states. Taken together, these calculations provide necessary information for estimating the switching time. All density functional theory calculations in this work are performed with Vienna Ab-initio Software Package (VASP),8,9 using the generalized gradient approximation (GGA) of Perdew-Burke-Enzerhof (PBE).10 Wave func-
Figure 1. Cartoons illustrating the structure and components [2]rotaxane molecule. (a) [2]rotaxane molecules, after.1 The [2]rotaxane molecule is composed of a backbone and an encircling cyclobis(paraquat-p-phenylene) (CBPQT) ring. The tetrathiafulvalene (TTF) unit is highlighted green and the dioxynaphthalene (DNP) unit red in this figure. In addition to these major components, the [2]rotaxane molecule also consisted of a sacrificial segment (also highlighted in green in the figure) at the very top and a binding moiety (light blue) at the very bottom. (b) A schematic description of the OFF-state of the molecule, where the CBPQT-ring is sitting at the TTF, and (c) shows the ON-state, where the ring moves to the DNP. The four orange dots in (b) and (c) correspond to the four PF6- counterions that reside in the vicinity of the [2]rotaxane molecule.
Figure 2. A likely reaction pathway for the shuttling of the CBPQTring along the molecular backbone during switching. Along this reaction coordinate, the ring is rotated by 90 and 50° as shown in the figure as it traverses from the TTF to the DNP.
tions are expanded in plane-wave basis sets up to an energy cutoff of 400 eV; projector augmented wave (PAW) pseudopotentials replace the core electrons.11 The [2]rotaxane molecule and its four accompanying counterions, a total of 174 atoms, are centered in a 20 Å × 20 Å × 45 Å supercell that is periodically repeated in all three dimensions with an intermolecular spacing of approximately 10 Å. Γ-point Brillioun zone sampling is used for all calculations. The system OFF-state, defined as where the CBPQT ring sits at the TTF station, is relaxed until Hellmann-Feynman forces on all atoms are less than 0.01 eV/Å. The atomic positions of four hexafluorophosphate (PF6-) counterions are concomitantly optimized in the vicinity of the CBPQT ring to satisfy the unpaired electron from the nitrogen. A similar relaxation procedure is performed for the ON-state configuration with the CBPQT ring residing at the DNP station. Relaxed atomic geometries of both the OFF- and ON-states are displayed in the Supporting Information. The configurations used in this study are in good agreement with previous work.3 3226
Figure 3. Computed energy landscape of the “shuttling” reaction for the [2]rotaxane molecule with (black) and without (gray) the PF6- counterions.
Having established the OFF- and ON- state structure of [2]rotaxane, the energetic barrier, and the activation energy, Ea, that must be overcome for the CBPQT, ring to shuttle from TTF to DNP is investigated. Seven static atomic configurations along the trajectory shown in Figure 2 are chosen. The total energy for each atomic configuration is determined after the ionic positions are relaxed until their forces are less than 0.01 eV/A along directions perpendicular to the reaction coordinate. Figure 3 shows the energy landscape along which the CBPQT ring shuttles from the TTF to the DNP as the molecule switches. A barrier of about 600 meV is found to separate the two stable states, which agrees reasonably with.7 The OFF-state has a lower energy than the ON-state, in agreement with experimental reports.2 As mentioned above, these calculations are performed on a system that includes the backbone of the [2]rotaxane molecule, the CBPQT ring, and four PF6- counterions. However, upon [2]rotaxane monolayer formation, the presence and arrangement of these counterions has not been definitively established. Previous work2 estimated the lateral footprint of the molecule to be 140 Å2; another work reported monolayers as dense as 54 Å2/molecule.12 (The latter is hard to reconcile even in the absence of the counterions.) Both numbers raise questions about the presence of PF6-. When the [2]rotaxane molecules are assembled into a monolayer, these anions inevitably face strong electrostatic repulsive forces from those of neighboring molecules, leading to an energetically unfavorable situation. The questions raised by prior reports prompt our study of the [2]rotaxane molecule in the absence of PF6-. Without the counterions, the energy landscape, overlaid in Figure 3, would have a minimum with the CBPQT ring lying about midway between the TTF and the DNP. In order for the [2]rotaxane molecule to behave as claimed and experimentally observed, some counterions would be needed in the vicinity of the molecule to neutralize the CBPQT ring. For all subsequent calculations, all four counterions are retained. Nano Lett., Vol. 9, No. 9, 2009
According to a previously proposed switching mechanism,1,7 the [2]rotaxane molecule, more precisely the TTF constituent, is oxidized to 1+ state by an external bias, which then repels the CBPQT-ring and shuttles to DNP. To better capture the role played by charging in the shuttling process, the IPs of the [2]rotaxane molecule are computed and compared to the 600 meV barrier, shown in Figure 3. Using total energy differences (the ∆SCF method),13 the gas-phase first and second IPs of the molecule are found to be IP1(CBPQT@TTF) ) 5.9 eV, IP1(CBPQT@DNP) ) 5.2 eV, IP2(CBPQT@TTF) ) 12.8 eV, and IP2(CBPQT@DNP) ) 10.8 eV. Care is taken to eliminate spurious monopole, dipole, and quadrapole interactions between supercells and to converge our results with respect to supercell size. The same method results in a gas-phase IP of benzene of about 9.6 eV within 2% of the experimental value.14 Inclusion of spin-polarization is found to have an insignificant effect on the above values and therefore is neglected in this work. Similarly, environmental polarization effects, which can reduce electron addition and removal energies for small molecules in contact with electrodes,15 were estimated with a simple image charge formula to be roughly 100 meV and thus neglected (see Supporting Information for details). Polarization from adjacent molecules within the monolayer would be expected to reduce the IP by less than this amount and is thus also neglected. Although [2]rotaxane IPs have been discussed previously, an assumption was made that the IPs of the [2]rotaxane molecule could be determined from gas-phase calculations of the isolated TTF and DNP constituents,1 an approximation we find to be inadequate here. It is found that when the [2]rotaxane molecule is charged, the electron is not simply removed from the TTF unit, but an appreciable redistribution of charge density is observed over the entire molecule (see Supporting Information for details). In light of the present results, which indicate the IPs are significantly larger than previously reported, a different switching mechanism is suggested. The energy difference between IP1(CBPQT@TTF) and the conduction band minimum of the silicon electrode is estimated to be about 1.9 eV, large compared to the 600 meV barrier described above. This suggests the ring should shuttle without the molecule being charged. Further, a +2 V bias on the silicon electrode will lower the activation energy to 400 meV (assuming a uniform drop across the molecule), enhancing the probability of shuttling. A finer mapping of the energy landscape about the OFF-state gives an estimate of the Arrhenius attempt frequency A, which we compute to be 1.4 × 1012 s-1 (see Supporting Information for details). Together with Ea, the rate constant, k ) Ae- Ea/kT, yields the shuttling time, tshuttle, to be 0.17s at equilibrium and 3.7 µs when a +2 V bias is applied on the silicon electrode. Because of the short shuttling time, the new switching mechanism proposed here does not contradict any of the previously reported cyclic voltametry (CV) measurements. In fact, if the CBPQT ring shuttled without charging, the oxidation experimentally reported at 0.5 V bias16 could be explained by a 0.1 eV difference between the IP of the ONstate and the gold work function at that bias (compare to Nano Lett., Vol. 9, No. 9, 2009
the 0.8 eV difference between the IP of the OFF-state and the gold work function). In addition to the shuttling time, a complete model of the switching time of a crossbar memory array requires consideration of the RC time constant associated with the circuit. The delay associated with the critical path is given by the Elmore delay model17 tRCC ) C1R1 + C2(R1 + R2) + ···+Cn(R1 + R2 + ···Rn)
where R is the resistance of the electrodes and can be estimated from the bulk resistivity and the dimensions of the electrodes. For the 160k-bit [2]rotaxane crossbar memory array of Green et al.,18 these quantities are readily available. However, to evaluate C, the total capacitance, the dielectric properties of the [2]rotaxane molecule are needed. These can be obtained by direct application of an electric field across a unit cell containing the [2]rotaxane molecule. The “local” dielectric constant, εr, is then defined from the ratio of the external applied field to the screened field inside the molecule, determined self-consistently with our density functional theory calculations, that is εr )
Escreened Eext
Figure 4 shows a plot of the local dielectric constant, defined as above, as a function of position along the long axis of the [2]rotaxane molecule. The variations in local dielectric constant can be understood from the different species along the backbone responding differently to the applied electric field. Viewing the [2]rotaxane molecule as many capacitors of different εr connected in series, effective dielectric constant, εreff, of the [2]rotaxane molecule as a whole is then evaluating as the harmonic mean, or εreff )
T t1
(∑ ) 1 εr
-1
where T is the total thickness of the dielectric, and ti is the thickness of each slice with a local dielectric constant of εr. Using the above equation, εreff of the [2]rotaxane in its OFFand ON-state are found to be 1.8 and 2.0, respectively. Repeating these calculations at different densities and extrapolating the computed values of the effective dielectric constant to the reported density, effective dielectric constants of 1.8 and 2.2 are obtained for the OFF- and ON-state (see Supporting Information for details). Using εreff ) 1.8, tRC is found to be 7 ns for the 160k-bit [2]rotaxane crossbar memory array, about 3 orders of magnitude less than tshuttle. Taken together, these numbers imply the system switching rate will be largely dominated by the shuttling time of the CBPQT-ring for any reasonably sized array. In light of these results, we comment on the applicability of this molecule as memory. First, since the energy landscape curvature at the DNP valley is similar to that for TTF, the memory cells would lose its bit within less than about a tenth 3227
Figure 4. The computed local dielectric constant as a function of position along the backbone. The effective dielectric constant, εreff, for (a) the OFF-state is 1.8 while that of (b) the ON-state is 2.0. These results are obtained from the 20 Å × 20 Å × 45 Å supercells, as described in the text.
Figure 5. A plot of switching time against array size for several different pitches, compared with the SNAP technique of.14
of a second, as the activation energy for the backward shuttling reaction is even smaller than the 600 meV calculated for the forward reaction. This classifies this system as a volatile memory. However, comparing to traditional volatile memories such as DRAM, the microsecond switching time scale severely limits the application of this molecule. While experimentally observed values of retention time and shuttling time would likely differ from these theoretical calculations due to various nonidealities within the experimental system and due to approximations made herein, it is reasonable to expect that the order-of-magnitude ratios of retention time and shuttling time of the memory would be similar for experimental and theoretical systems, since the mechanisms involved in the two phenomena are similar. Thus, longer retention times in the real systems would be achieved at the expense of degraded programming speed, and vice versa. Additionally, our calculations indicate that with conventional photolithography, instead of having a 160k-bit crossbar array comfortably switching at the optimum of about 4 µs, a smaller 100k-bit memory array would only just be able to switch at this intrinsically shuttling-limited switching time. The superlattice nanowire pattern transfer (SNAP) technique, a unique approach not accessible to many researchers, was employed to fabricate the memory array in ref 18; Figure 5 shows the switching time as a function of array size comparing SNAP to three other conventional photolithography technologies. With a 1 µm patterning tool, 3228
the array size would need to be reduced by 3 orders of magnitude to retain a similar RC time constant. Note that the propagation delay associated with the address decoder is ignored in these calculations. To conclude, the switching mechanism of the [2]rotaxane molecule has been studied in this work with first principles density functional theory calculations. Several physical properties related to the switching time of this system are computed, and from these calculations a new switching mechanism for the [2]rotaxane molecule is suggested. We propose that upon applying a +2 V bias, the OFF-state conformation is no longer energetically favorable, and the energy barrier to the ON-state is reduced, resulting in the [2]rotaxane molecule switching to a configuration with the CBPQT ring at the DNP station. By carefully mapping the energy landscape of the [2]rotaxane molecule at its OFFstate, an Arrhenius prefactor is estimated. This yielded a 0.17 s and 3.7 µs shuttling time of the CBPQT-ring at equilibrium and when bias is applied, respectively. Further, using the computed dielectric constant, the bulk resistivity of the electrodes and the dimensions of the crossbar memory array are reported,17 and the RC delay for the 160k-bit crossbar demonstrated is found to be about 7 ns, which adds insignificantly to the total switching time. Because of the long shuttling time, future use of this molecule as a volatile memory (without chemical modification or external coupling) will be limited. Acknowledgment. This work was funded by the Materials, Structures, and Devices Focus Center under the auspices of the Focus Center Research Program. Work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. We also acknowledge NERSC for providing computational support. Supporting Information Available: This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Jang, Y. H.; Goddard, W. A. Mechanism of oxidative shuttling for [2]rotaxane in a Stoddart-Heath molecular switch: Density functional theory study with continuum-solvation model. J. Phys. Chem. B 2006, 110, 7660–7665. Nano Lett., Vol. 9, No. 9, 2009
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